Thermoelectric transport of mesoscopic conductors coupled to voltage and thermal probes

TL;DR

This paper studies how inelastic scattering affects the thermopower of phase-coherent mesoscopic conductors, revealing that it reduces thermopower and induces magnetic-field asymmetry, with implications for nanoscale thermoelectric devices.

Contribution

It introduces a model using an additional probe to simulate inelastic scattering and uncovers the magnetic-field asymmetry in the Seebeck coefficient caused by inelastic processes.

Findings

Inelastic scattering reduces thermopower.

Inelastic processes generate magnetic-field asymmetry.

Thermopower fluctuations diminish with more probe modes.

Abstract

We investigate basic properties of the thermopower (Seebeck coefficient) of phase-coherent conductors under the influence of dephasing and inelastic processes. Transport across the system is caused by a voltage bias or a thermal gradient applied between two terminals. Inelastic scattering is modeled with the aid of an additional probe acting as an ideal potentiometer and thermometer. We find that inelastic scattering reduces the conductor's thermopower and, more unexpectedly, generates a magnetic-field asymmetry in the Seebeck coefficient. The latter effect is shown to be a higher-order effect in the Sommerfeld expansion. We discuss our result using two illustrative examples. First, we consider a generic mesoscopic system described within random matrix theory and demonstrate that thermopower fluctuations disappear quickly as the number of probe modes increases. Second, the asymmetry is explicitly calculated in the quantum limit of a ballistic microjunction. We find that asymmetric scattering strongly enhances the effect and discuss its dependence on temperature and Fermi energy.